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How to Find the Sum of Two Cubes

Spotting a distribution that results in the sum of two cubes is a shortcut to solving distribution problems. To recognize what distribution results in the sum of two cubes, look to see if the distribution has a binomial, (a + b), which is the sum between two terms, multiplied by a trinomial,

which has the squares of the two terms and the opposite of their product.

The binomial has a plus sign and the middle term in the trinomial has a minus sign.

Here's an example:

a + b is the binomial and is the sum between two terms because it has a plus sign (+).

The trinomial has the squares of the two terms

and is opposite the product of the two terms.

Here are some examples to give you a better understanding.

Example 1: The sign in the binomial is +, so the answer has a +. The cube of 4 is 64.

Example 2: The opposite of the product of 6 and 5yz is –30yz.